Can I use the minimax optimization algorithm for multiple variables?

In my problem, I set 3 separate threshold values which are then used to group my dataset in four sub-groups. Then I calculate mean values or sums in specific variables of the subgroups.

Can I use the minimax algorithm to find the optimized (minimum) 3 thresholds, that will give me the maximum values of the specific sums and means that I am looking for?

Answer 1

[John D'Errico]

If your goal is to set thresholds which are then used to group your data into subgroups, the answer is no. Sorry. Why?

Think about it. Change the threshold just by a tiny amount. As long as it does not change what subgroups the data falls in, it changes nothing about your objective. So your function becomes a piecewise constant function of the parameters, thus discontinuous, non-differentiable, etc. No optimizer will handle this well, certainly not one that assumes differentiability.

So, it is not a problem to have multiple unknowns for that optimizer. What you cannot have is a discontinuous function. You also cannot solve for multiple VARIABLES. Group all of your unknowns into ONE vector of unknowns.

[Emmanouil Barmpounakis]

Thank you for your immediate reply.

Actually, as I have 'imagined' the solution to my problem, there is a thin line between optimization and sensitivity analysis, as I think you are suggesting in a way.